Experimental and numerical study of self- and solute diffusion in Zr-Sn alloys

Abstract

In this work, experimental measurements were performed to determine the diffusion coefficient of Sn in hexagonal closed-packed (HCP) Zr and to analyze the evolution of the lattice parameters in Zr–Sn HCP alloys. A statistical analysis of the experimental data produces a diffusion coefficient of Sn in Zr at 750 ◦C of approximately 1 × 10−18 m2/s, with values as low as 8 × 10−19 m2/s, depending on alloy purity and composition. These values are close to those of the reported self-diffusion coefficients of pure HCP Zr, indicating a weak perturbation of the diffusion process by Sn. To support and interpret the experimental findings, density functional theory (DFT) calculations were carried out to investigate vacancy-mediated solvent and solute diffusion. Calculations were performed within the generalized gradient approximation using VASP and complemented by MEAM-based simulations with LAMMPS. The transport coefficients were evaluated using the five-, eight-, and thirteen-frequency models. Comparison between experimental and calculated diffusion coefficients demonstrates that the five-frequency model–comprising five independent jump frequencies and neglecting pair dissociation and anisotropic effects–is sufficient to reproduce the observed diffusion behavior, whereas the eight- and thirteenfrequency models lead to significant deviations, particularly for solute diffusivity. Accordingly, the analysis is formulated within a vacancy-mediated substitutional framework to assess the consistency with Hood’s criterion, with the results indicating vacancy-mediated substitutional diffusion as the most consistent transport mechanism under the present conditions.